Definition, Formula and Physical interpretation of Cross Product.
The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.
The cross product is defined by the formula
where:
is the angle between and in the plane containing them (hence, it is between 0° and 180°)
and are the magnitudes of vectors and
and is a unit vector perpendicular to the plane containing and , in the direction given by the right-hand rule .
If the vectors and are parallel (that is, the angle θ between them is either 0° or 180°), by the above formula, the cross product of and is the zero vector
If is a positively oriented orthonormal basis, the
The cross product is used to describe the Lorentz force experienced by a moving electric charge
Since velocity force and electric field are all true vectors, the magnetic field is a pseudovector.
The moment of a force applied at point B around point A is given as:
The angular momentum of a particle about a given origin is defined as:
where is the position vector of the particle relative to the origin, is the linear momentum of the particle.
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